Role of Symmetry in the Self Assembly of Space-Filling Honeycombs

The self-assembly of hard polyhedral particles is driven by the maximization of entropy. As particles are forced into increasingly dense configurations, the system seeks states with maximal entropy, which are often ordered crystalline structures. The notion of directional entropic forces - statistical forces that promote particles to bind or align in certain directions - have been developed to support observations that facets on particles can mimic covalent bonds in atomic crystals. Within this framework, we set out to design particles that would self-assemble into honeycombs, or space-filling arrangements of polyhedra, that are isostructural to atomic crystals. We use the Voronoi tessellation to generate hard, space-filling polyhedra, or “Voronoi particles,” that are guaranteed to stabilize the target structure at infinite pressure, analogous to designer potentials that stabilize arbitrary crystals structures with complex radially symmetric potentials. We characterize the thermodynamics, kinetics and self-assembly behavior of these polyhedra and demonstrate how an understanding of the role of symmetry and particle shape can guide design to improve assembly behavior.